# Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields

created by bruè on 09 Jun 2018

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Submitted Paper

Inserted: 9 jun 2018
Last Updated: 9 jun 2018

Pages: 18
Year: 2018

Abstract:

The aim of this note is to prove a sharp regularity estimate for solutions of the continuity equation associated to vector fields of class $W^{1,p}$ with $p>1$. Regularity is understood with respect to a log-Sobolev functionals, that could be seen as a version of the Gagliardo semi-norms measuring the logarithmic derivative'' of a function.